@article{Elleuch2026, 
author = {Zied Elleuch and Younes Brahim Oumedjber and Omar Kahouli and Adel Ouannas and Sulaiman Almohaimeed and Lilia El Amraoui and Mohamed Ayari},
title = {Incommensurate fractional epidemic dynamics with compartment-specific memory, treatment response, and physics-informed forecasting},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22316-22353},
keywords = {incommensurate fractional order, Caputo derivative, SEIATR model, epidemic dynamics, L1 scheme, physics-informed neural network, forecasting},
url = {https://www.sciopen.com/article/10.3934/math.2026903},
doi = {10.3934/math.2026903},
abstract = {This paper develops an incommensurate fractional-order susceptible-exposed-symptomatic infectious-asymptomatic infectious-treated-recovered (SEIATR) model with compartment-specific Caputo memory. We establish local well-posedness, positivity, boundedness, biological feasibility, disease-free and endemic equilibria, and the basic reproduction number. Local stability is analyzed through the rational-order incommensurate Matignon criterion. A componentwise multi-order L1 scheme is then used for simulation, refinement, and sensitivity analysis. Finally, a physics-informed neural network is employed as a synthetic benchmark for hidden-state reconstruction, parameter and order identification, residual checking, and short-horizon forecasting. The results show that compartment-specific memory mainly affects peak timing, persistence, and treatment load, whereas epidemiological rates govern amplification and threshold behavior.}
}